Deriving Coulomb's law and other fundamental equations from F=ma?

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Discussion Overview

The discussion centers around the possibility of deriving fundamental equations related to electricity and magnetism from Newton's second law, F=ma. Participants explore the implications of such derivations and the limitations of classical mechanics in explaining electromagnetic phenomena.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant questions whether it's possible to derive electricity and magnetism from Newton's second law, referencing a humorous suggestion from a physics class.
  • Another participant asserts that it is not possible to derive concepts such as the charge of an electron or the behavior of like and unlike charges from Newton's equations.
  • A different viewpoint suggests that while Newton's laws cannot derive electromagnetism, the scalar and vector potentials are necessary for understanding electromagnetic phenomena through quantum mechanical principles.
  • One participant proposes that the original joke may have been referring to deriving aspects of classical mechanics rather than electromagnetism.

Areas of Agreement / Disagreement

Participants generally disagree on the possibility of deriving electromagnetic principles from Newton's laws, with some asserting it is impossible while others suggest alternative frameworks for understanding electromagnetism.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the applicability of classical mechanics to electromagnetic theory and the dependence on quantum mechanical concepts for a complete understanding.

Queequeg
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I saw a joke crib sheet for a physics class that said "F=ma, derive the rest," but is it actually possible to derive at least electricity and magnetism questions from Newton's second law?
 
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No, you can't derive electricity and magnetism from Newton't equations. For example, there is no way the charge on an electron could be derived, nor could the fact that like charges repel and unlike charges attract, and nor could the fact that a varying magnetic field induces a current in a wire.
 
Queequeg said:
I saw a joke crib sheet for a physics class that said "F=ma, derive the rest," but is it actually possible to derive at least electricity and magnetism questions from Newton's second law?

Not from Newton's law. But both the scalar and vector potentials are required if one demands the covariance of, say, Schrödinger's equation under local phase transformations of the wavefunction. Electromagnetism is ultimately explainable by a fundamentally quantum mechanical symmetry.
 
Perhaps they were just talking about deriving most of classical mechanics.
 

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